The PM will say "we now all need to hold our nerve" to get the changes needed to get her Brexit deal through Parliament by the 29 March deadline.
She added: "Jeremy Corbyn's letter to the Prime Minister this week makes clear our unequivocal opposition to a no-deal Brexit, the Prime Minister's current deal or any tweaked version of it, a CETA style deal or any deal that could lead to a hard border in Northern Ireland".
But EU leaders insist the legally binding withdrawal agreement can't be changed. She will tell Parliament she still believes it is possible to get a deal that MPs can support.
Mrs May's announcement of returning to update MPs on 26 February and then more votes on 27 February - if she has still not got a final deal - meant Thursday's expected "high noon" for Mrs May had probably been postponed.
There appears little prospect of an imminent breakthrough with Brussels, and Mrs May might not bring her deal back for a decisive vote this month.
Theresa May has offered further talks with Labour in an attempt to secure cross-party support for a Brexit deal.
But Mrs May responded: "In most circumstances, that period may be important in order for this House to have an opportunity to study that agreement".
The prime minister is aiming to allay lawmaker concern that, unless they vote to take control of the process and order her to seek an extension of European Union negotiations, they will have lost their chance to avoid a no-deal Brexit.
Winning the confidence ballot 200 votes to 117, May acknowledged that a "significant number" of Conservatives had voted against her.
Or it may well not.
The Act, passed by the coalition government in 2010, requires 21 sitting days before the ratification of any worldwide treaty.
No date has been set for the next meeting, but the letter concludes with Mrs May saying she looked forward to the two parties meeting "as soon as possible".
The Prime Minister says there is no need to negotiate a customs union as her deal provides for the benefits of being in one.
British Secretary of State for International Trade Liam Fox, Swiss Federal Councillor Guy Parmelin and Liechtenstein's Foreign Minister Aurelia Frick shake hands after signing a trade agreement in Bern, Switzerland.
Prime Minister is expected to issue a rallying call for MPs to "hold our nerve" as her battle to secure a Brexit deal backed by Parliament reaches a crucial stage.
"We aren't going to reopen the withdrawal agreement", Barnier said after the meeting, which was described by a United Kingdom spokesman as "constructive".
So, in practice, if she wants to push this vote later, and later, then only to the very last minute (and remember the European Union doesn't want to budge until then), that bit of legislation might not be a block, because if MPs approve it, she can get round it. He said Mrs May's agreement would achieve most of Mr Corbyn's goals without preventing independent trade deals.
"I don't see that in the letter", he said.
MPs and peers, including former ministers Phillip Lee, Sam Gyimah, Guto Bebb and Lord Willetts said her current Brexit deal "risks further dividing our nation and costing jobs" and is "highly unlikely" to benefit families and communities.
The government has tabled an amendable motion for debate on Thursday, seeking the House's continued support for the prime minister to demand "alternative arrangements" on the controversial Irish backstop. What progress has she made on identifying and working up the alternative arrangements?
"Construction, production and services output fell in the month (of December), the first time that there has been such a broad-based fall in monthly output since September 2012", the ONS said.